Constant mean curvature n-noids in hyperbolic space

TL;DR

This paper constructs genus zero constant mean curvature surfaces with multiple ends in hyperbolic space using the DPW method, expanding the class of known solutions in differential geometry.

Contribution

It introduces a novel application of the DPW method to generate Alexandrov-embedded CMC surfaces with arbitrary Delaunay ends in hyperbolic space.

Findings

Successfully constructs new CMC surfaces with multiple ends

Demonstrates the versatility of the DPW method in hyperbolic geometry

Extends the catalog of known constant mean curvature surfaces

Abstract

Using the DPW method, we construct genus zero Alexandrov-embedded constant mean curvature (greater than one) surfaces with any number of Delaunay ends in hyperbolic space.